7 6 Mr. La xs Method of -finding the Latitude of a Place , 
an altitude of the sun is taken at the distance ae from the meri- 
dian, but that, in consequence of an error in the assumed latitude, 
the calculated time is ag ; and that, with a lat. differing from 
the former by one minute, we compute again, and the time is 
found equal to af ; then will the area gc be to gb as one mi- 
nute to the whole error in latitude. Let another altitude be 
taken at the distance ae. from noon, and let the times com- 
puted with the two different latitudes that were employed be- 
fore be ag and af; then, in this case likewise, the area gc will 
be to the area gb, as one minute to the error in latitude. Now 
the latter curve is the “ fgura. tan gentium f whose quadrature 
is given by Cotes, in his Harmonia Mensurarum, and the ex- 
pression for which is extremely simple. For the fluxion of the 
area is = -, and the area itself = log. 1 + ^ = log. se- 
cant of the angle at the pole. The difference of the log. secants, 
or log. cosines, will of course be equal to the area intercepted 
betwixt the tangents which correspond to them. 
Hence a table might easily be constructed with a double argu- 
ment, — the distance from noon, and the variation in time arising 
from' the different suppositions of latitude, — which might imme- 
diately exhibit the logarithm of the area corresponding to any 
particular base eg supposed to be given. A second table might 
have for its argument the difference of the logarithms of the area 
gb and the area gc, (which is likewise conceived to be known) 
and discover at once, in degrees, minutes, and seconds, the cor- 
rection to be made in the assumed latitude. This correction, as it 
appears from a comparison of the signs of L and z in the equa- 
tion L = xTz, must be added or subtracted, according as the 
distance from noon obtained by computation is too great or too 
